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Paper IPM / Physic / 6530  


Abstract:  
In this paper we first characterize the Lie algebra of derivations of the
threedimensional Manin quantum space as the semidirect product of the
Lie algebra of its inner derivations and the threefold generalized Virasoro
algebra with central charge zero. Then we consider Hamiltonian systems on the
quantum plane and we prove that the set of Hamiltonian derivations is a
Virasoro algebra with central charge zero. Moreover, we show that the
only possible motions on the quantum plane come from quadratic Hamiltonians
and we find the solutions of the corresponding Hamilton equations explicitly.
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